This morning, I had a discussion with a friend of mine about a game he is developing.
I explained that playing “perfect” strategy would be nearly impossible due to some subtle complexities of the way the game is played. As a result of this, the game would not likely play anywhere near its “theoretical” payback.
Many games have this problem. Blackjack pays 99.5%, but very few players play anywhere near this. Ultimate Texas Hold’em has a payback well into the 99% range, too, but stats from the casinos make it clear very few players, if any, can manage this high of a payback.
My friend stated he thought he would be able to play the game close to the theoretical because he is an accomplished poker player. I asked him if he was an accomplished video poker player and he said he wasn’t.
I told him any table game against a dealer was really nothing more than playing video poker and had no resemblance to poker. You see, poker is about reading players, understanding their betting patterns and their tells.
Video poker is about one thing – math. There is no one to bluff. All that matters is what is the probability of all final hands given what I choose to discard. Let’s take a look at a simple example: 5-spades, 5-diamonds, 6-club, 7 hearts, 8 diamonds.
In theory, there are 32 ways to play this hand, but I think we can quickly rule out 29. I don’t think anyone is seriously going to consider holding only the off-suit 6-8 or holding all 5 cards (which would result in an immediate loss).
There are really only three possibilities, two of which are identical. The player can either hold the pair of 5’s or the 4-card Straight (hence, the two identical possibilities as it doesn’t matter which 5 the player keeps.)
If the player keeps the 4-card Straight eight cards will result in a straight and the rest in a loss. So, if we add up the total payout, we’d have 8 straights at 4 units each for a total of 32 units. There are 47 possible draws. We divide the 32 by 47 to get 0.68. This is called the Expected Value (or EV) of this hand using this possible discard strategy.
Calculating the Expected Value of holding the pair is a bit more complex, but easy enough to calculate using a computer. There are 16,215 possible draws if the player holds two cards. We look at these possible draws and at the final hands.
The player can wind up with a Four of a Kind, Full House, Three of a Kind or Two Pair. We add up the total payout of all of these winning hands and divide by 16,215. The result is an EV of 0.82.
This Expected Value is greater than that of the 4-card Straight, so the proper play is to hold the Low Pair. When playing video poker (and virtually every other casino game), the proper play is to follow the one with the highest EV.
You don’t go with a “hunch” that a 5 is coming up or you just feel a 4 or a 9 is going to fill out that Straight. There is a distinct probability of each of these events occurring and we use those probabilities to our advantage. This is what allows a player to achieve the theoretical playback of a game.
It is an advantage because most players don’t play this way. Because of this, the casinos can off the games with a relatively high payback, knowing they can rely on human error to pad their profits. For the players who play according to the math, they have the advantage of being able to play to the theoretical payback over the long run.
Mastering video poker takes some significant effort. The strategy is complex and learning whether to hold the Low Pair or the 4-card Straight is merely one example of a strategy where if you play by what you think is right that may in fact be quite wrong.
The good news is thanks to guys like me, the toughest part of learning the strategy (creating it) has already be done for you. The next step is learning that strategy and putting it to practical use.
We’ll save more of that for next week.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].